In 200 BC, the ancient Greek mathematician Archimedes first gave the correct solution of π in theory. He used the perimeter of circumscribed and inscribed polygons to approach the perimeter of a circle from large and small directions, and skillfully obtained π.
Around 150 BC, Ptolemy, another ancient Greek mathematician, used the chord table method (the chord length of the central angle 1 multiplied by 360 and then divided by the diameter of the circle) to give the approximate value of π 3. 14 16.
In 200 AD, Liu Hui, a mathematician from China, provided a scientific method to find pi, which embodied extreme views. Liu Hui's method is different from Archimedes's. He only takes "internal connection" instead of "external connection". Using the inequality of circular area, he gets twice the result with half the effort. Later, Zu Chongzhi took the lead in calculating pi and got the "reduction rate". π& lt； 3. 14 15927. Unfortunately, Zu Chongzhi's calculation method was later lost. It is speculated that he used Liu Hui's cyclotomy, but what method he used is still a mystery.
/kloc-in the 5th century, the Islamic mathematician Al Cassie calculated the perimeters of three regular 2-sided polygons inscribed and circumscribed by a circle respectively, and pushed the π value to16th place after the decimal point, breaking the record kept by Zu Chongzhi for thousands of years.
1579, a relational expression was discovered in Veda, France.
In 1650, Varis expressed π as the product of finite elements.
Later, Leibniz discovered it, and then Euler proved that although these formulas are simple in form, they require a lot of calculation. The biggest breakthrough in the calculation method of π value is to find its expression of arc tangent function.
1706, the British mathematician Laura Mai first discovered that its calculation speed far exceeded the classical algorithm.
1777, the French mathematician Buffon put forward his famous problem of throwing needles. Through it, we can get the over-similarity value by probability method. Suppose we draw a set of parallel lines with a distance of, and throw a needle with a length of at will on this plane. If the number of throwing needles is, the number of times that any parallel line crosses is, many people have done experiments, 190 1 year.
Legendre proved that π is an irrational number in 1794, that is, it cannot be expressed by the ratio of two integers.
1882, the German mathematician Linmand proved that π is a transcendental number, that is, it cannot be the root of an algebraic equation with integral coefficients.
After 1950s, the calculation of pi began with the help of computer, which led to a new breakthrough. At present, some people claim that pi has been calculated to hundreds of millions or even billions of significant digits.
People try to know statistically whether the number of π digits has some regularity. The game is still on. As someone said, the process of mathematicians' exploration is also like π: endless and endless. ...